摘要翻译：
设$\γ$是极化复射影流形$(M,L)$的自同构。然后，$\gamma$对$l$的$k$次张量幂的全局全纯截面空间的自同构$\gamma_k$,对于每$k=1,2,...$；对于$k\gg0$，Lefschetz不动点公式用不动点数据表示$\gamma_k$的迹。更一般地说，我们可以考虑$\gamma_k$与Toeplitz算子的组合，该算子与$M$上的光滑函数相关联。更一般地，在紧致连通李群保持$(M，L，\gamma)$的相容作用存在时，我们可以考虑与$G$的不可约表示相关的等变和上的诱导线性映射。本文在辛约化理论中常见的假设下，证明了这些映射的迹允许一个渐近展开式为$k\~+\infty$,并计算了它的先导项。
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英文标题：
《Szego kernels, Toeplitz operators, and equivariant fixed point formulae》
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作者：
Roberto Paoletti
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Complex Variables        复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics        数学
二级分类：Symplectic Geometry        辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
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英文摘要：
  Let $\gamma$ be an automorphism of a polarized complex projective manifold $(M,L)$. Then $\gamma$ induces an automorphism $\gamma_k$ of the space of global holomorphic sections of the $k$-th tensor power of $L$, for every $k=1,2,...$; for $k\gg 0$, the Lefschetz fixed point formula expresses the trace of $\gamma_k$ in terms of fixed point data. More generally, one may consider the composition of $\gamma_k$ with the Toeplitz operator associated to some smooth function on $M$. Still more generally, in the presence of the compatible action of a compact and connected Lie group preserving $(M,L,\gamma)$, one may consider induced linear maps on the equivariant summands associated to the irreducible representations of $G$. In this paper, under familiar assumptions in the theory of symplectic reductions, we show that the traces of these maps admit an asymptotic expansion as $k\to +\infty$, and compute its leading term.
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PDF链接：
https://arxiv.org/pdf/0707.1375